A New Direction in AI--Toward a Computational Theory of Perceptions:
Reflecting the bounded ability of the human brain to resolve detail, perceptions are intrinsically imprecise. In more concrete terms, perceptions are f-granular, meaning that (1) the boundaries of perceived classes are unsharp; and (2) the values of attributes are granulated, with a granule being a clump of values (points, objects) drawn together by indistinguishability, similarity, proximity, and functionality. F-granularity of perceptions puts them well beyond the reach of traditional methods of analysis based on predicate logic and/or probability theory. The computational theory of perceptions (CTP) that is outlined here adds to the armamentarium of AI a capability to compute and reason with perception-based information. The point of departure in CTP is the assumption that perceptions are described by propositions drawn from a natural language. In CTP, a proposition, p, is viewed as an answer to a question and the meaning of p is represented as a generalized constraint. To compute with perceptions, their descriptors are translated into what is called the Generalized Constraint Language (GCL). Then, a goal-directed constraint propagation is employed to answer a give query. A concept that plays a key role in CTP is that of precisiated natural language (PNL).
The computational theory of perceptions suggests a new direction in AI--a direction that may enhance the ability of AI to deal with real-world problems in which decision-relevant information is a mixture of measurements and perceptions. What is not widely recognized is that many important problems in AI fall into this category.
Precisiated Natural Language (PNL):
It is a deep-seated tradition in science to view the use of natural languages in scientific theories as a manifestation of mathematical immaturity. The rationale for this tradition is that natural languages are lacking in precision. However, what is not widely recognized is that adherence to this tradition carries a steep price--the inability to exploit the richness of natural languages in a way that lends itself to computation and automated reasoning.
In a significant departure from existing methods, the high expressive power of natural languages is harnessed by a process termed precisiation. In essence, if p is proposition in a natural language (NL), then precisiation of p results in a representation of the meaning of p in the form of what is referred to as a generalized constraint. With these constraints serving as basic building blocks, composite generalized constraints can be generated by combination, constraint propagation, modification, and qualification. The set of all composite generalized constraints and associated rules of generation and interpretation constitute the Generalized Constraint Languages (GCL). Translation from NL to GLC is governed by the constraint-centered semantics of natural languages (CSNL). Thus, through CSNL, GCL serves as precisiation language for NL. Precisiation Natural Language (PNL) is a subset of NL, which is equipped with constraint-centered semantics and is translatable into GLC. By construction, GCL is maximally expressive. In consequence, PNL is the largest subset of NL, which admits precisiation. The expressive power of PNL is far greater than that of conventional predicate-logic-based meaning-representation languages.
The concept of PNL opens the door to a significant enlargement of the role of natural languages in scientific theories and, especially, in information processing, decision, and control. In these and other realms, a particularly important function that PNL can serve is that of a concept definition language--a language that makes it possible to formulate precise definitions of new concepts and redefine those existing concepts that do not provide a good fit to reality.
Perception-Based Decision Analysis (PDA):
Decisions are based on information. More often than not, the information available is a mixture of measurements and perception. The problem with perceptions is that they are intrinsically imprecise. A concept that plays a key role in perception-based decision analysis is that of precisiated natural language, PNL. In PDA, precisiated natural language is employed to define the goals, constraints, relations, and decision-relevant information. An important sublanguage of PNL is the language of fuzzy if-then rules, FRL. In this language, a perception of a function, f, is described by a collection of fuzzy if-then rules. Such a collection is referred to as the fuzzy graph of function f. Employment of PNL in decision analysis adds an important capability--a capability to operate on perception-based information. The capability has the effect of substantially enhancing the ability of DA to deal with real-world problems. More fundamentally, the high expressive power of PNL opens the door to a redefinition of such basic concepts as optimality and causality. Perception-based decision analysis represents a significant change in direction in the evolution of decision analysis. As we move farther into the age of machine intelligence and automation of reasoning, the need for a shift from computing with numbers to computing with words, and from manipulation of measurements to manipulation of perceptions, will cease to be a matter of debate.
From Computing with Numbers to Computing with Words to Computation with Perceptions--A Paradigm Shift:
The theory put forth in this research is focused on the development of what is referred to as the computational theory of perceptions (CTP)--a theory that comprises a conceptual framework and a methodology for computing and reasoning with perceptions. The base for CTP is the methodology of computing with words (CW). In CW, the objects of computation are words and propositions drawn from a natural language. The point of departure in the computational theory of perceptions is the assumption that perceptions are described as propositions in a natural language. Furthermore, computing and reasoning with perceptions is reduced to computing and reasoning with words.
To be able to compute with perceptions it is necessary to have a means of representing their meaning in a way that lends itself to computation. Conventional approaches to meaning representation cannot serve this purpose because the intrinsic imprecision of perceptions puts them well beyond the expressive power of predicate logic and related systems.
In the computational theory of perceptions, representation of meaning is a preliminary to reasoning with perceptions--a process that starts with a collection of perceptions that constitute the initial data set (IDS) and terminates in a proposition or a collection of propositions that play the role of an answer to a query, that is, the terminal data set (TDS).
The principal aim of the computational theory of perceptions is the development of an automated capability to reason with perception-based information. Existing theories do not have this capability and rely instead on conversion of perceptions into measurements--a process that in many cases is infeasible, unrealistic, or counterproductive. In this perspective, addition of the machinery of the computational theory of perceptions to existing theories may eventually lead to theories that have a superior capability to deal with real-world problems and make it possible to conceive and design systems with a much higher MIQ (Machine IQ) than those we have today.